In one-way slabs, the loads are transferred directly to the opposite supports in the short direction (50%) to each support. In two-way slabs, loads are transferred to the beams (four beams) by bisecting the slab angles with 45 degrees lines, and the resulting areas will triangular on the short beams and trapezoidal on the long beams.
Depends on the type of beam/slap system. Generally speaking, for cast in situ RC beam-slab grids, compatibility torsion at the beams is neglected due to cracking and thus no fixed end moments are typically considered to be transferred from the slabs to the beams. In this case, simplified load distribution can be obtained by considering the approximate yield lines at ultimate limit state of the slab (basically the criterion mentioned by the immediately previous answer).
In other cases, such as a bridge deck slab supported by monolithic prestressed girders, transfer of torsion (end moments of the slab) should be considered. A simple idea is to model the deck slab as a grid of equivalent beams and assign deck load to those; care must be taken to release horizontal shear transfer of the deck grid to the beams (if eccentric to reflect relative centroid spacing) so as not to interfere with beam normal stresses (when modelled as T-beam to account for shear lag).
In the first instance you do not need a 3D finite element analysis to analyze a slab beam system. A 2D finite element analysis will do just fine. In such analysis the plan should be divided into rectangular elements but the beam elements will have different D from slab elements. The calculated shear forces will indicate how the slab transfers load to slabs. In a FEA it is unnecessary to have a format for transferring load from slab to beams. The load transfer will be part of the results.